Each of the main characters in The House of Hades have been tested for different reasons and to test their strengths. As these characters are tested the grow and evolve to better accompany each other as a good group. At the start they were enemies and were reluctant to work as a team with the opposite group (being Roman and Greek). An example would be Frank defeating the katobleps which are these cow things that will poison you if they breathe near you. They also have a poisonous look that makes you freeze if you look into their eyes. He did this to save two of the other crew members and which one he did not like but saved him still because he was a very important crew member and learned to tolerate each other. In the book the trust is shown to be bonded when Jason who is scared of Nico trusts him “Nico drank from the chalice, then offered it to Jason. "You asked me about trust, and taking a risk? Well, here you go, son of Jupiter. How much do you trust me?" Frank wasn't sure what Nico was talking about, but Jason didn't hesitate. He took the cup and drank.”
In the book the main idea is for the group to close the doors of death. Rick Riordan (the author) brings this idea up by following the end of the last book The Mark of Athena which leaves with Percy and Annabeth falling into Tartarus who ends up turning out to be a god. One of the main problems was that they needed to close the doors of death from both sides - Tartarus and the mortal world - and to do this they would need to have people in Tartarus to be there to do it when the other people in the mortal world do it because they need to do it at the same time. So by following up from the last book exactly from where they started this book they already addressed most of the main idea. The book had many side quests like getting Diocletian’s staff and getting things that they need to get for the battle with Gaea it just makes the book all the more memorable.